Xenharmonic Wiki

130edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Francium (talk | contribs)
4,831 edits
→Music: +music
ArrowHead294 (talk | contribs)
15,215 edits
mNo edit summary
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 130 factors into 2 × 5 × 13, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}.
Since 130 factors into {{nowrap|2 × 5 × 13}}, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}.


[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.
[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.
Line 324: Line 324:


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 3136/3125, 19683/19600
| 2401/2400, 3136/3125, 19683/19600
| {{mapping| 130 206 302 365 }}
| {{mapping| 130 206 302 365 }}
| -0.119
| &minus;0.119
| 0.311
| 0.311
| 3.37
| 3.37
Line 344: Line 336:
| 243/242, 441/440, 3136/3125, 4000/3993
| 243/242, 441/440, 3136/3125, 4000/3993
| {{mapping| 130 206 302 365 450 }}
| {{mapping| 130 206 302 365 450 }}
| -0.241
| &minus;0.241
| 0.370
| 0.370
| 4.02
| 4.02
Line 351: Line 343:
| 243/242, 351/350, 364/363, 441/440, 3136/3125
| 243/242, 351/350, 364/363, 441/440, 3136/3125
| {{mapping| 130 206 302 365 450 481 }}
| {{mapping| 130 206 302 365 450 481 }}
| -0.177
| &minus;0.177
| 0.367
| 0.367
| 3.98
| 3.98
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
Note: temperaments supported by [[65edo|65et]] are not included.  
Note: temperaments supported by [[65edo|65et]] are not included.  


{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 434: Line 420:
|-
|-
| 2
| 2
| 54\130<br>(11\130)
| 54\130<br />(11\130)
| 498.46<br>(101.54)
| 498.46<br />(101.54)
| 4/3<br>(35/33)
| 4/3<br />(35/33)
| [[Bischismic]]
| [[Bischismic]]
|-
|-
| 5
| 5
| 27\130<br>(1\130)
| 27\130<br />(1\130)
| 249.23<br>(9.23)
| 249.23<br />(9.23)
| 81/70<br>(176/175)
| 81/70<br />(176/175)
| [[Hemipental]]
| [[Hemipental]]
|-
|-
| 10
| 10
| 27\130<br>(1\130)
| 27\130<br />(1\130)
| 249.23<br>(9.23)
| 249.23<br />(9.23)
| 15/13<br>(176/175)
| 15/13<br />(176/175)
| [[Decoid]]
| [[Decoid]]
|-
|-
| 10
| 10
| 54\130<br>(2\130)
| 54\130<br />(2\130)
| 498.46<br>(18.46)
| 498.46<br />(18.46)
| 4/3<br>(81/80)
| 4/3<br />(81/80)
| [[Decal]]
| [[Decal]]
|-
|-
| 26
| 26
| 54\130<br>(1\130)
| 54\130<br />(1\130)
| 498.46<br>(9.23)
| 498.46<br />(9.23)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Bosonic]]
| [[Bosonic]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Scales ==
== Scales ==
{| class="wikitable"
{| class="wikitable"
|+14-tone temperament of "Narrative Wars"<br>as an example of using 130edo:
|+ style="font-size: 105%;" | 14-tone temperament of "Narrative Wars"<br />as an example of using 130edo:
|-
! Step
! Step
! Cents
! Cents
! Distance to the nearest JI interval<br>(selected ratios)
! Distance to the nearest JI interval<br />(selected ratios)
|-
|-
| 13 (13/130)
| 13 (13/130)
Line 490: Line 477:
| 9 (47/130)
| 9 (47/130)
| 433.846
| 433.846
| [[9/7]] (-1.238 ¢)
| [[9/7]] (&minus;1.238 ¢)
|-
|-
| 7 (54/130)
| 7 (54/130)
Line 502: Line 489:
| 9 (76/130)
| 9 (76/130)
| 701.538
| 701.538
| [[3/2]] (-0.417 ¢)
| [[3/2]] (&minus;0.417 ¢)
|-
|-
| 7 (83/130)
| 7 (83/130)
Line 514: Line 501:
| 5 (101/130)
| 5 (101/130)
| 932.308
| 932.308
| [[12/7]] (-0.821 ¢)
| [[12/7]] (&minus;0.821 ¢)
|-
|-
| 13 (114/130)
| 13 (114/130)
Line 522: Line 509:
| 7 (121/130)
| 7 (121/130)
| 1116.923
| 1116.923
| [[21/11]] (-2.540 ¢)
| [[21/11]] (&minus;2.540 ¢)
|-
|-
| 9 (130/130)
| 9 (130/130)
| 1200.000
| 1200.000
| [[Octave]] (2/1, ±0 ¢)
| [[Octave]] (2/1, 0 ¢)
|}
|}


Line 544: Line 531:
[[Category:Hemischis]]
[[Category:Hemischis]]
[[Category:Hemiwürschmidt]]
[[Category:Hemiwürschmidt]]
[[Category:Listen]]
[[Category:Sesquiquartififths]]
[[Category:Sesquiquartififths]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/130edo"